It is not easy to spot flaws in your design as, even if you have many browsers installed on your computer, you will almost certainly not have access to every browser on every platform.
You can use services such as BrowserCam (http://www.browsercam.com) to view your MediaWiki skin's design in multiple browsers without needing access to different operating systems:
Note
Although BrowserCam is not a free service, you can try it for a limited period with a free trial.
BrowserCam also allows you to see the design as it would be displayed on different devices, including Blackberry handheld devices and other PDAs (personal digital assistants).
If you are redesigning an existing wiki, a cheaper alternative could be to ask a smaller portion of your wiki's community to test a new design before you release it to your live website. Alternatively, you can ask friends and family to test the design on as many different computers and browsers as possible.